One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
Can you make a cycle of pairs that add to make a square number
using all the numbers in the box below, once and once only?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
Can you use this information to work out Charlie's house number?
Think of a number, square it and subtract your starting number. Is
the number you’re left with odd or even? How do the images
help to explain this?
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
In 1871 a mathematician called Augustus De Morgan died. De Morgan
made a puzzling statement about his age. Can you discover which
year De Morgan was born in?
Add the sum of the squares of four numbers between 10 and 20 to the
sum of the squares of three numbers less than 6 to make the square
of another, larger, number.
Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?
Does a graph of the triangular numbers cross a graph of the six
times table? If so, where? Will a graph of the square numbers cross
the times table too?
The discs for this game are kept in a flat square box with a square
hole for each disc. Use the information to find out how many discs
of each colour there are in the box.
Find another number that is one short of a square number and when
you double it and add 1, the result is also a square number.
Can you make square numbers by adding two prime numbers together?
Complete the magic square using the numbers 1 to 25 once each. Each
row, column and diagonal adds up to 65.
A square patio was tiled with square tiles all the same size. Some
of the tiles were removed from the middle of the patio in order to
make a square flower bed, but the number of the remaining tiles. . . .
A woman was born in a year that was a square number, lived a square
number of years and died in a year that was also a square number.
When was she born?
Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?
What is the value of the digit A in the sum below: [3(230 + A)]^2 =
Use the interactivities to complete these Venn diagrams.
How many four digit square numbers are composed of even numerals?
What four digit square numbers can be reversed and become the
square of another number?
Using your knowledge of the properties of numbers, can you fill all the squares on the board?